Finite Group Databasebeta

← #20245050

Subgroups — #20245050

Order 6016.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689671C211yesmaximal, characteristic
2#15689095C212yesmaximal, complemented
3#15688917C212yesmaximal, complemented
4#15688916C211yesmaximal, characteristic, complemented
5C47×#353C211yesmaximal, characteristic, complemented
6C2×#10625352C411yescharacteristic, complemented
7C2×#10625352C2211yescharacteristic
8#13094024C411yescharacteristic, complemented
9#13094011C411yescharacteristic, complemented
10#13094011C2211yescharacteristic
11#13093995—22no—
12D4×Dic47—22no—
13#13093980—22no—
14C42×D47C411yescharacteristic, complemented
15#13093939C2212yes—
16#13093938—22no—
17#127×C47C2211yescharacteristic
18#99×C47C2212yes—
19C2×D4×C47—22no—
20C2×D4×C47C2×C411yescharacteristic
21C2×D4×C47C2311yescharacteristic
22C2×C22⋊D47—21no—
23C2×C22⋊D47D412yes—
24C22×Dic47—21no—
25C22×Dic47D412yes—
26#10625352—41no—
27#10625352—41no—
28#10625352—41no—
29#10625352—41no—
30C2×C4×D47—21no—
31C2×C4×D47C2×C411yescharacteristic
32C2×Dic94C2×C411yescharacteristic
33C2×Dic94C2×C411yescharacteristic
34C22⋊C4×C47—22no—
35C42×C47C2×C411yescharacteristic
36C22⋊Dic47—22no—
37C22⋊Dic47—22no—
38C22⋊Dic47—22no—
39C4⋊Dic47—22no—
40Dic47⋊C4—42no—
41C4×Dic47—21no—
42C4×Dic47—42no—
43C4×Dic47C2×C411yescharacteristic
44C23×C47—21no—
45C23×C47C2×D412yes—
46C22×D47C22⋊C411yescharacteristic
47D4×C47—41no—
48D4×C47—41no—
49D4×C47—44no—
50C2×C4×C47—21no—
51C2×C4×C47—42no—
52C2×C4×C47C22×C411yescharacteristic
53C22⋊D47—42no—
54C22⋊D47—42no—
55C2×Dic47—22no—
56C2×Dic47—22no—
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—41no—
60C2×Dic47—41no—
61C2×Dic47—42no—
62C2×Dic47C22⋊C412yes—
63C2×Dic47C22⋊C411yescharacteristic
64C4×D47—21no—
65C4×D47—21no—
66C4×D47—42no—
67Dic94—41no—
68Dic94—41no—
69C22×C47—22no—
70C22×C47—42no—
71C22×C47—42no—
72C22×C47—41no—
73C22×C47C2×C22⋊C411yescharacteristic
74C2×D47—21no—
75C2×D47—41no—
76C4×C47—22no—
77C4×C47—21no—
78C4×C47—82no—
79Dic47—22no—
80Dic47—41no—
81Dic47—41no—
82Dic47—82no—
83Dic47#9911yescharacteristic
84Dic47#9911yescharacteristic
85#2126—471nomaximal, Sylow
86C2×C47—21no—
87C2×C47—42no—
88C2×C47—81no—
89C2×C47C2×#9911yescharacteristic
90D47—41no—
91#532—471no—
92#410—472no—
93#354—472no—
94#353—471no—
95#353D4711yescharacteristic, complemented
96C47#212611yescharacteristic, complemented, Sylow
97C2×#41—471no—
98C2×#41—471no—
99C4⋊Q8—471no—
100#127C2×D4711yescharacteristic
101#124—471no—
102#124—471no—
103#121—942no—
104C4×D4—942no—
105#117—942no—
106C2×C42—471no—
107#99—472no—
108#99—942no—
109#99C2×D4712yes—
110#41—1881no—
111#41—1881no—
112#41—1881no—
113#41—1881no—
114C2×Q8—471no—
115C2×Q8—471no—
116C2×D4—22no—
117C2×D4—472no—
118C2×D4—941no—
119C2×D4C4×D4711yescharacteristic
120C2×D4C22×D4711yescharacteristic
121C22×C4—472no—
122C22×C4—471no—
123C22×C4—941no—
124C22×C4—941no—
125C4⋊C4—942no—
126C4⋊C4—1882no—
127C22⋊C4—22no—
128C22⋊C4—942no—
129C22⋊C4—942no—
130C22⋊C4—942no—
131C42—471no—
132C42—941no—
133C42—1882no—
134C42C4×D4711yescharacteristic
135C23—21no—
136C23—471no—
137C23D4×D4712yes—
138Q8—1881no—
139Q8—1881no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—1882no—
144D4—1882no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—471no—
148C2×C4—472no—
149C2×C4—941no—
150C2×C4—941no—
151C2×C4—942no—
152C2×C4—942no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—1882no—
156C2×C4—1881no—
157C2×C4—1881no—
158C2×C4—1882no—
159C2×C4C2×C4×D4711yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—941no—
165C22—1881no—
166C22C22⋊C4×D4711yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—471no—
171C4—471no—
172C4—942no—
173C4—3762no—
174C4—1881no—
175C4—1881no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—1881no—
180C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#353C2
socleC2×C47C2×#99
hypercenter#353D47
hypocenterC47#2126
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #15689095C2semidirect
3. #15688917C2semidirect
4. #15688916C2semidirect
5. C47×#353C2semidirect
6. C2×#10625352C4semidirect
8. #13094024C4semidirect
9. #13094011C4semidirect
14. C42×D47C4semidirect
95. #353D47semidirect
96. C47#2126semidirect